DETROIT — The family of a former U.S. Marine imprisoned in Iran since his 2011 arrest on spying charges is hopeful that he could be released soon because of recent developments in his case, including his conviction for a lesser offense, a family spokesman said Sunday.

Iran arrested Amir Hekmati, now 31, in August 2011 while he was on a trip to visit his grandmothers in Tehran. He was born in the U.S. and holds dual Iranian and U.S. citizenship.

Iran’s government labeled Hekmati a CIA spy, and a court sentenced him to death after finding him guilty of espionage. Iran’s Supreme Court overturned the sentence in 2012, but Hekmati has remained behind bars.

His family and the U.S. government have repeatedly said that Hekmati was not a spy and that his visit was for personal reasons, because of the illness of one grandmother.

Last week, the family learned that Hekmati had been tried secretly in a Revolutionary Court, convicted of the less serious offense of “cooperating with hostile governments” and sentenced to 10 years in prison, said family spokesman Chris Hayes.

Hekmati’s new defense lawyer, Mahmoud Alizadeh Tabatabaei, appears to be well connected with the Iranian government and optimistic that Hekmati could be released after completing one-third of his sentence, or about three years, family spokesman Chris Hayes said.

“It’s a good change,” Hayes told The Associated Press in a telephone interview. “All of this is, with the new lawyer, all good.”

Interviewed in Iran on Saturday, Tabatabaei told AP that he was seeking Hekmati’s conditional release from Evin prison, north of the capital, Tehran.

“According to law, if someone serves one-third of his conviction period and within that time, shows an acceptable behavior in jail, he can be entitled to conditional freedom,” Tabatabaei said. “One-third of his imprisonment will end around September and October.”

A conditional release could allow Hekmati to leave the country, depending on what a court decides. That could allow Hekmati to visit his father, Ali Hekmati, who is a professor in Michigan. Family members say Ali Hekmati has been diagnosed with terminal brain cancer and recently suffered a stroke.